Strong Lateral Velocity Variations Research Articles

Fourier finite‐difference migration for steeply dipping reflectors with complex overburden1

AbstractThe improvement in accuracy and efficiency of wave‐equation migration techniques is an ongoing topic of research. The main problem is the correct imaging of steeply dipping reflectors in media with strong lateral velocity variations. We propose an improved migration method which is based on cascading phase‐shift and finite‐difference operators for downward continuation. Due to these cascaded operators we call this method‘Fourier finite‐difference migration’(FFD migration).In our approach we try to generalize and improve the split‐step Fourier migration method for strong lateral velocity variations using an additional finite‐difference correction term. Like most of the current migration methods in use today, our method is based on the one‐way wave equation. It is solved by first applying the square‐root operator but using a constant velocity at each depth step which has to be the minimum velocity. In a second step, the approximate difference between the correct square‐root operator and this constant‐velocity squareroot operator (the error made in the first step) is implemented as an implicit FD migration scheme, part of which is the split‐step Fourier correction term.Some practical aspects of the new FFD method are discussed. Its performance is compared with that of split‐step and standard FD migration schemes. First applications to synthetic and real data sets are presented. They show that the superiority of FFD migration becomes evident by migrating steeply dipping reflectors with complex overburden having strong lateral velocity variations. If velocity is laterally constant, FFD migration has the accuracy of the phase‐shift method. The maximum migration angle is velocity adaptive, in contrast to conventional FD migration schemes. It varies laterally depending on the local level of velocity variation. FFD migration is more efficient than higher‐order implicit FD schemes. These schemes use two cascaded downward‐continuation steps in order to attain comparable migration performance.

Tomographic inversion for the seismic velocity structure beneath northern New England using seismic refraction data

The seismic velocity structure of the crust and the upper mantle beneath northern New England was investigated from the travel time data of the 1984 Maine Seismic Refraction Profile and the 1988 Ontario‐New York‐New England Seismic Refraction Profile seismic refraction experiments by using tomographic inversion techniques. Strong lateral seismic velocity variations were found in the upper 15 km of the crust, and these variations are correlated with regional geologic and tectonic structures. The Grenville basement in the Adirondack Mountains of eastern New York is characterized by an unusually high P wave velocity of 6.7 km/s in the upper 15 km of the crust. This high‐velocity basement extends eastward below western Vermont to a depth between 15 and 20 km from the surface. More typical upper crustal P wave velocities of 5.6 to 6.4 km/s were generally found in central and southern Maine and in New Hampshire, and the anisotropic upper crustal zone west of Penobscot Bay in Maine was imaged by locally slower velocities. The correlation of the inversion velocity structure with the tectonic features of northern New England shows that the Appalachian mountains in northern New England may extend, tectonically, to at least 20 km deep in the crust. The velocity distribution at 20 km depth shows three northeast elongate juxtaposed belts which correspond to the Connecticut Valley‐Gaspe Synclinorium, the Bronson Hill Anticlinorium and the Kearsarge‐Central Maine Synclinorium, respectively. The Connecticut Valley‐Gaspe and Kearsarge‐Central Maine Synclinoria have relatively high velocities from 6.94 to 7.12 km/s while the Bronson Hill Anticlinorium has relatively low velocities from 6.52 to 6.75 km/s in the lower crust. Another low‐velocity area of 6.52 km/s at 20 km depth is imaged beneath the White Mountain Batholith in central New Hampshire and may be a lower crustal expression of this batholith. Upper mantle velocity structures were obtained for the Grenville basement, the Appalachians in northern New England and the Avalon terrane in southeastern Maine from the long‐range seismic refraction data. Generally, the older Grenville lithosphere (about 1100 Ma) in Quebec has higher velocity in the upper mantle than does the younger Avalon terrane (no older than 650 Ma) in the southeastern part of northern New England. The data suggest that the velocity of the upper mantle beneath the old North American craton increases stepwise with observable velocity discontinuities in depth, while that beneath the Avalon terrane does not increase through the first 40 km of the upper mantle. The data analysis also shows that the upper mantle suture between the Grenville basement and the Avalon terrane occurs in a narrow belt beneath the Appalachian mountains of central Maine and New Hampshire. The did of the Moho discontinuity beneath northern New England is modeled as nearly flat as 0.7° in the N57°W direction and as steep as 1.2° beneath the Grenville basement.

Observations of direct P-wave slowness and azimuth anomalies for teleseisms recorded in Long Valley caldera, California

Abstract Using particle motion, frequency-wavenumber analysis, and planewave fitting, we observe large anomalies in the bearing and apparent velocity of 0.5 to 1.0 Hz teleseismic P-waves incident at stations near the resurgent dome of Long Valley caldera, California. Our 3-component regional and teleseismic data come from three 2-mo deployments: (1) a 10 station, 2.9-km aperture array, (2) a 5 station, 1.9-km aperture array, and (3) a 3 station network, spanning about 5 km. We find stacked particle motion to be the most informative polarization method when the signal-to-noise ratio (SNR) is high and wavefronts are nonplanar. However, the insensitivity of the broadband frequency-wavenumber method (BBFK) to noise makes it more useful as SNR declines. Numerical simulations and data analyses using the BBFK method show that for a 10 station, 3-km aperture array, precision of roughly 8° in bearing and 0.008 sec/km in apparent slowness can be obtained with average teleseismic data in regions having complex structure. Bearing anomalies at Long Valley caldera reach up to 124°, whereas apparent slowness differ from expected values by up to a factor of 2. The anomalies are most likely caused by strong lateral velocity variations in the subcaldera crust between depths of 6 to 35 km.

MODEL‐BASED STACK: A METHOD FOR CONSTRUCTING AN ACCURATE ZERO‐OFFSET SECTION FOR COMPLEX OVERBURDENS1

AbstractThe interpretation of stacked time sections can produce a correct geological image of the earth in cases when the stack represents a true zero‐offset section. This assumption is not valid in the presence of conflicting dips or strong lateral velocity variations. We present a method for constructing a relatively accurate zero‐offset section. We refer to this method as model‐based stack (MBS), and it is based on the idea of stacking traces within CMP gathers along actual traveltime curves, and not along hyperbolic trajectories as it is done in a conventional stacking process. These theoretical curves are calculated for each CMP gather by tracing rays through a velocity‐depth model. The last can be obtained using one of the methods for macromodel estimation. In this study we use the coherence inversion method for the estimation of the macromodel since it has the advantage of not requiring prestack traveltime picking. The MBS represents an accurate zero‐offset section in cases where the estimated macromodel is correct. Using the velocity–depth macromodel, the structural inversion can be completed by post‐stack depth migration of the MBS.

Inversion Techniques to Enhance Images of the Subsurface

Seismic surveys are commonly used in the exploration for oil and hydrocarbons. However, in some regions of Australia, strong lateral velocity variations in the subsurface material tend to obscure the seismic images. Nowadays, the major problem associated in the production of seismic images of the subsurface is the availability of reliable subsurface velocities that can be inverted from routinely collected reflection data. This paper presents a technique for inverting two-way travel times and stacking velocities from such data sets to model the subsurface velocities. We model the subsurface by a number of layers of material separated by laterally varying boundaries; the velocities within each layer also vary laterally. We seek the smoothest possible functions describing the lateral variation in interval velocities and boundary location which also fit the observations to a specified tolerance. That is, we permit a trade-off between the smoothness of the model and goodness of fit to the data. Data are weighted according to the accuracy with which they are acquired; this causes the residual at each data point to be compared with its expected error. We represent the interval velocity and boundary location for each layer as a sum of B-splines, and develop a non-linear inversion technique to model subsurface velocities. This algorithm is applied to reflection data from the Gippsland Basin using various interpretations of the stacking velocity data. It is found that the velocity profiles obtained have some significant differences compared with those predicted by the Dix formula, and yet generally seem to be more consistent with well data than previous velocity models. In particular, the method presented here seems able to handle velocity inversions better than earlier techniques. Furthermore, this technique provides a more objective way of determining an appropriate coarse-scale velocity model to be used in the migration of seismic data than traditional methods of smoothing Dix results.

Upper mantle velocity structure in the Mediterranean and surrounding regions from seismological data

Upper mantle velocity structure in the Mediterranean and surrounding regions has been studied in detail to a depth of 500 km by analysis of P- and S-wave travel-time data of 229 deep earthquakes. P- and S-wave velocities, obtained “at the depths of foci” by using Kaila's (1969) analytical method, in the intermediate and deep earthquake regions of the Calabrian arc-Tyrrhenian Sea, western Mediterranean-southern Spain, western and southern margins of the Balkan peninsula and the Vrancea region of the eastern Carpathian reveal lateral velocity variations of the order of 3–4% down to 150 km depth, the P velocities in the Balkan margins being the highest. In the Calabrian arc-Tyrrhenian Sea deep earthquakes region, the P velocity increases from 8.01 km/s at 40 km to 8.14 km/s at 210 km depth. The P velocity increases rapidly at deeper depths from 210 km with a gradient of 0.005 s −1, reaching 9.62 km/s at 500 km depth. The S velocity in this region increases from 4.58 km/s at 40 km to 4.73 km/s at 400 km depth without any indication of a zone of rapid velocity increase. However, the S velocity in the Calabrian arc-Tyrrhenian Sea deep earthquakes region is found to be about 6% higher than the average S velocity of 4.34 km/s in the top 150–200 km of the surrounding upper mantle region as deduced from surface waves dispersion studies. Similarly, the S velocities in the intermediate earthquake regions of the western Mediterranean and the Balkan margins are found to be about 5% higher than the corresponding average values in the surrounding upper mantle regions. These variations are essentially due to the presence of a well delineated sub-lid low S velocity channel extending over most of central Europe. The P velocity model for the Calabrian arc-Tyrrhenian Sea deep earthquakes region, determined in the present study, agrees remarkably well with the P velocity models EKW (England et al., 1977) and MR (Mayer-Rosa and Mueller, 1973) which are applicable for the upper mantle beneath south-central Europe. A comparison of the P velocity models in south-central Europe, including that of the present study, with the P velocity models SNE (Hurtig et al., 1979), KCA (King and Calcagnile, 1976) and MA (Masse and Alexander, 1974) which are applicable for the upper mantle beneath the east European platform reveals strong lateral velocity variations in the upper mantle beneath the two regions. The velocities in south-central Europe are about 5% lower than those in the east European platform to a depth of at least 250 km. These results are consistent with the temperature-depth functions for Europe given by Stromeyer (1978) which show 400°–500°C higher temperatures at depths in central Europe than those in the east European platform. The nearly constant S velocity of 4.6–4.7 km/s from 40 to 400 km depth in the Calabrian arc-Tyrrhenian Sea deep earthquakes region, as determined in the present study, is also consistent with the higher temperatures expected in the surrounding upper mantle region beneath central Europe. The “400 km discontinuity” has not been revealed by both P- and S-wave velocity models down to 500 km depth in the present study, possibly due to its larger depth of 520–540 km in south-central Europe, in comparison to its relatively shallow depth of 380–420 km in the east European platform as given by several models. Alternatively, the high P-wave velocity gradient from 210 to 500 km depth may imply absence of a “sharp” 400 km discontinuity which is probably replaced by a broad transition zone in this region.

Subsurface imaging of the Garlock Fault, Cantil Valley, California

Imaging of the Garlock fault from seismic reflection data tests tectonic models for the Mojave Desert region of southern California. Models developed from geologic and geodetic evidence of fault movement rates disagree on whether the Garlock fault should dip north or south. Such models are further at odds with focal mechanism and dislocation analyses consistent with a vertical strike‐slip fault. Our analysis demonstrates a nonvertical, southward dip for the Garlock fault. Consortium for Continental Reflection Profiling Mojave line 5 collected seismic reflection data across the Garlock in Cantil Valley, where the 3‐km‐deep Cantil pull‐apart basin has developed between the southwest and east branches of the fault. We analyze the reflection data for evidence of the fault's structure to 5 km depths. Garlock fault plane reflections on unprocessed shot gathers merge with the first arrival as the source progresses to the surface trace of the east branch, explicitly tracing the Garlock fault as a seismic reflector from depth to the mapped contemporary fault trace. The apparent velocity of these reflections gives a 37°±10° south dip for the east branch of the fault. A prestack Kirchhoff sum migration images the east branch reflector with a 45° south dip. Our migration process fully accounts for the bending of seismic rays through the strong lateral velocity variations in Cantil basin. The south dip of the Garlock's east branch together with basement steps that decrease to the south suggest that Cantil basin developed from a 0.4–1 mm/yr component of extension normal to the fault. Development of the basin by detachment provides a mechanism to widen it as left‐lateral motion lengthens it, allowing the pull‐apart to maintain the globally constant length‐to‐width ratio of 3. Detachment by the Garlock at Cantil Valley similarly requires 0.4–1 mm/yr of dextral strike slip on a northwest striking fault such as the Helendale that cuts the Mojave between the Garlock and Pinto Mountain faults. Such motion is consistent with regional tectonic models.

Quantitative Evaluation of Dynamic Time-Shifts for Correcting Seismic Data

Large lateral velocity changes, particularly those associated with sea-floor topography, can severely distort seismic stack sections, for example, under the submarine canyons in the Gippsland Basin in Bass Strait. Conventional replacement statics partially correct these problems, but are usually inadequate in situations where the sea-floor variation is severe or the water is deep. Dynamic corrections calculated by ray-tracing through the region of strong lateral velocity variation give improved results.Dynamic corrections derived by ray-tracing can be evaluated by analyzing t2 -y2 plots where t is time and y is offset within CMP gathers. This facilitates making the following comparisons: (1) the zero-offset time before and after dynamic correction; (2) the RMS velocities (calculated using zero-offset rays traced in the model) with normalized stacking velocities after dynamics; (3) hyperbolic moveout before and after dynamics. A similar evaluation of conventional replacement statics provides a reference for evaluating the ray-tracing derived ‘replacement dynamics’.Ray-tracing requires a subsurface model which can be difficult to construct in areas of structural complexity. This is often the case near submarine canyons. A simple model using water depth and a single marker horizon or datum when ray-traced to derive replacement dynamics gives significant improvement with respect to the conventional statics solution in submarine canyon areas. Errors in velocity can be reduced by as much as 50% and errors in hyperbolic moveout reduced by about 70%.

Depth sections and interval velocities from surface seismic data

First of all, what is the nature of the problem to be addressed here? Conventional seismic processing consists of unstacked reflection seismic data as input and, typically, a CDP stacked section in time as output. Except for extremely simple situations, a time migrated section will also be formed. The problem is that the time structure on that final section does not necessarily represent the true depth structure in the earth. This is particularly true when strong lateral velocity variations are present.

Lithosphere thickness in the contact zone of the Moldanubicum and Saxothuringicum in central Europe

The analysis of the time residuals of P waves and their 3-D inversion show strong lateral velocity variations beneath the GRF array, situated above the contact zone of two important tectonic units; the Saxothuringicum and Moldanubicum. Variations of teleseismic P residuals have provided data for constructing a detailed model of the lithosphere-asthenosphere boundary in the region. Assuming the effects of lateral changes of average velocities in the subcrustal lithosphere to be much smaller than the effects of lithosphere thickness variations, we relate the changes of representative average residuals in direct proportionality to changes of the lithosphere thickness. Under this assumption we can explain the variations of average residuals over the GRF array by a relatively high increase in the thickness of the lithosphere of about 50 km from the northernmost to the southernmost stations. The lithosphere-asthenosphere boundary dips steeply to the SSE and the isopachyte contours follow the general direction of the Variscan fold belt in central Europe, fitting a general pattern of the lithosphere thickness derived for central Europe.

SHEAR‐WAVE REFLECTION PROFILING FOR NEAR‐SURFACE LIGNITE EXPLORATION*

ABSTRACTWe present the results of a shear‐wave reflection experiment and in situ measurements in opencast lignite exploration. Near‐surface coal seams have lower shear‐wave velocities (∼ 200 m/s) and lower densities than sand and clay layers. Due to strong reflection coefficients, a shear‐wave reflection survey provides a powerful tool in lignite prospecting. Due to shorter seismic wavelengths shear waves will yield a higher resolution of shallow subsurface structure than compressional waves. Low shear‐wave velocities and strong lateral velocity variations, however, require a dense data acquisition in the field. The variation of stacking velocities can exceed ± 15% within a profile length of 300 m. The different steps in processing and interpretation of results are described with actual records. The final CMP‐stack shows steep‐angle fault zones with maximum dislocations of 20 m within a coal seam.

Migration with the full acoustic wave equation

Conventional finite‐difference migration has relied on one‐way wave equations which allow energy to propagate only downward. Although generally reliable, such equations may not give accurate migration when the structures have strong lateral velocity variations or steep dips. The present study examined an alternative approach based on the full acoustic wave equation. The migration algorithm which developed from this equation was tested against synthetic data and against physical model data. The results indicated that such a scheme gives accurate migration for complicated structures.